The present invention is directed to a method for improving the power of an axial gas laser with an excitation tube wherethrough a gas flows and to an axial gas laser with at least one excitation tube wherethrough gas is flowing and to an excitation tube for an axial gas laser.
The main part of an excitation tube of an axial gas laser is usually straight. In a function of the distance from the gas inlet there is generated by the gas stream a boundary layer on the inner wall of the tube caused by viscosity forces within the flowing gas or the gas mixture. Caused by this boundary layer the flow velocity of the gases viewed across the cross-section of the tube diminishes from a maximum value in the centre of the tube's cross-sectional area to zero at the tube wall region. The thickness of this boundary layer increases in flow direction. Thus there remains, in flow direction, subsequently less free space for the unobstructed flow of the gas so that, in flow direction, the gas velocity must increase for constant gas amount per time unit flowing through all tube cross-sectional areas. With an increasing gas velocity the viscosity forces do also increase and so does the boundary layer too so that the boundary layer increases in its thickness more than proportional along the length of the excitation tube. If in this excitation tube there is additionally applied heat to the gas or the gas mixture as it is done by electrically stimulating the gas, the gas density diminishes i.e. the gas volume rises and thus the flow velocity becomes higher which latter again favours the growth of the boundary layer. With respect to the gas velocity along the excitation tube three different cases may be considered:
(1) The gas flows into the straight tube with a velocity lower than sonic velocity and reaches exactly at its outlet sonic velocity.
(2) The gas flows with supersonic velocity into the tube and is decelerated to sonic velocity at the end of the tube.
(3) The gas flows with supersonic velocity into the tube and is decelerated by means of a compression shock to a velocity below sonic velocity and is then accelerated towards the end of the tube to sonic velocity.
By applying heat to the gas in all three cases there must be considered a velocity change from subsonic to supersonic velocity which latter velocity transition is physically not possible within a straight tube of constant cross-section. If the amount of heat applied reaches a critical value which would lead to said velocity transition of the gas there occurs the thermal chocking phenomenon, that is, the tube will be choked. The stopped gas flow does only restart after interruption of the heat appliance. Thus one is limited on usual axial gas lasers with such excitation tubes with respect to power introduction to the gas by physical occurrences and one is thus also limited with respect to the beam power reachable by such a gas laser.
It is an object of the present invention to provide a method as mentioned above to increase the power of an axial gas laser with an excitation tube wherethrough a gas flows. Thus with a given cross-sectional area of tube as for instance at the gas inlet zone of it, it is a target to enable that the gas may absorb more heat along its travel through the tube without being forced along the tube to a transition from subsonic velocity to supersonic velocity.
This is reached by the method for improving the power of an axial gas laser with an excitation tube wherethrough a gas flows whereby the effect of occurrence of a boundary layer on the tube inner wall as concerns reduction of the cross-sectional area of the tube wherethrough said gas may flow unobstructedly, is taken into account by changing the inner cross-sectional area of said excitation tube at least along an axial part of said excitation tube.
By changing the cross-sectional area of the tube the sectional area which is left "open" for the gas flow from the boundary layer is influenced and thus the resulting flow velocity of the gas is influenced. The changement of the cross-sectional area is determined according to desired characteristica of physical parameters along the length of the excitation tube. Such parameters are especially the pressure of the gas mixture, the gas mixture temperature and possibly and dependent therefrom, other parameters as the Mach number.
The characteristica of the parameters, desired along the tube's axis, are realized by determining the cross-sectional areas at least substantially as indicated from the formula set forth below thereby taking into account that usually the gas used is a gas mixture so that its state equation has to be also considered. ##EQU1## wherein, with introduction of an x-dependency as dependency from axial coordinate said tube:
F(x): is the flow cross-sectional area at locus x PA0 F.sub.1 : is the smallest flow cross-sectional area at locus x.sub.1 PA0 M(x): is the Mach number at locus x PA0 T.sub.01 : is the gas rest temperature PA0 k(x): is the isentropic exponent at the locus x PA0 c.sub.p (x): is the specific heat of the gas at locus x PA0 q.sub.2 : is the heat applied totally PA0 .xi.(x): is the heat applied at locus x relative to the totally applied heat q.sub.2 PA0 M.sub.1 : the Mach number at the smallest cross-sectional area at x.sub.1 along the tube
under consideration of the gas state equation of the gas or gas mixture used. It must be understood that if the heat absorbed by the gas is increased the boundary layer will increase. Such an increase of the boundary layer is inventively compensated for by spreading the excitation tube so that the flowing gas is not forced from sub- to supersonic velocity inspite of further absorption of heat. Evaluation of the expression according to the above formula, results for the special cases wherein the gas pressure or the gas temperature shall be constant along the length of the excitation tube is a changement of cross-sectional areas along at least a part of said excitation tube and in gas flow direction which is at least approximately linearly rising for gas pressure therealong being constant or at least approximately exponentally rising for temperature characteristic there along to be constant.
It is further an object of the invention to provide an axial gas laser with at least one excitation tube wherethrough gas is flowing in which it is possible to apply to said gas more power without the gas having to transition from subsonic or sonic velocity to supersonic velocity which object is reached by said axial gas laser comprising said excitation tube having an inner cross-section area which steadily changes at least along a part of the axial extent of said tube.
It is still a further object of the present invention to provide an excitation tube as mentioned above wherein gas turbulances with one single turbulance center over the cross-sectional area of the tube, said "wide-areal" turbulances, do not occur which is reached by said excitation tube having a flow cross-section departing from circular form.
It is a still further object of the present invention to provide for said gas laser then built as electrically excited laser, an electrode arrangement which does not disturb the flow of gas through said excitation tube which is reached by said gas laser comprising at least one electrode arrangement which lies substantially without forming a radial stop and/or a radial groove along the circumference of the inner wall of said excitation tube.
A further object of the invention is to provide the possibility to have said electrode arrangement disposed within the tube of changing cross-sectional area. This is reached by having said electrode arrangement comprising a conical inner bore to realize a changement of said inner cross-section area of said tube.
A still further object of the present invention is to provide an excitation tube for an axial gas laser which excitation tube gives the possibility to apply more heat to a gas used in such an axial gas laser thus having that gas absorb more thermal energy and thus allowing such a laser to develop more optical energy. This is reached by an excitation tube according to the present invention for an axial gas laser wherein the cross-sectional area of said tube steadily changes at least along the part thereof preferably growing towards one of the ends of said tube at least nearly linearly or exponentially.
Beside energy considerations it is important to ensure a uniform flow along the excitation tube. Any "wide-areal" turbulances with one center of turbulance across the respective cross-sectional areas of the tube should be avoided and in opposition thereto small areal turbulances which show several turbulance centers across respective cross-sectional areas of the tube should be maintained or generated because such "small-areal" turbulances improve the mixing effect of the gas throughout the excitation tube. Omission of such "wide-areal" turbulances and introduction of small areal turbulances is reached as mentioned above by providing cross-sectional areas of the excitation tube departing from circular shape being for instance of a triangular, four-angular or elliptical shape. By such a shape formation of "wide areal" turbulances is prevented and occurrence of small areal turbulances is improved.
If, as mentioned above, the inventive excitation tube has to be provided with an electrode arrangement, its provision without any stop and without any radial gap along the inner wall of the tube prevents again occurrence of "wide areal" turbulances. If the electrode is disposed in a region where inventively the cross-sectional area of the tube varies especially becomes larger, then the electrode arrangement is provided with an accordingly conical inner bore which fits as exactly as possible and without the mentioned stops and gaps along the inner wall of the tube.
Preferred embodiments and further objects of the invention will become evident from the examples which will now be described by way of figures.